Presentation on theme: "Produced by Karen, Patrik, Franklid and Janette – 7H ACCELERATION CLASS SMPK 4 PENABUR –"— Presentation transcript:
Produced by Karen, Patrik, Franklid and Janette – 7H ACCELERATION CLASS SMPK 4 PENABUR –
A quadrilateral is a polygon that has 4 sides, and four corners. If the interior angles are added up, the sum will be 360. Some quadilaterals are convex or concave. The origin of the word quadilateral is from two Latin words, quadri (a varient of four) and latus (sides).
What is a Rhombus? A rhombus is In Euclidean geometry, a rhombus or rhomb is a convex quadrilateral whose four sides all have the same length. The rhombus is often called a diamond, after the diamonds suit in playing cards, or a lozenge, though the latter sometimes refers specifically to a rhombus with a 45° angle.Euclidean geometryquadrilateraldiamondslozenge Every rhombus is a parallelogram, and a rhombus with right angles is a squareparallelogramsquare The English word "rhombus" derives from the Ancient Greek όμβος (rhombos), meaning "spinning top". The plural of rhombus can be either rhombi or rhombuses.Ancient Greek
Characteristics Of Rhombus Characteristics: A convex quadrilateral is a rhombus if and only if it is any one of The following:convexquadrilateralif and only if a parallelogram in which at least two consecutive sides are equal in length a quadrilateral with four sides equal in length a parallelogram in which a diagonal bisects an interior angle a quadrilateral in which each diagonal bisects two interior angles a parallelogram in which the diagonals are perpendicular a quadrilateral in which the diagonals are perpendicular and bisect each other
F ORMULA O F R HOMBUS P ERIMETER How to find the perimeter of a rhombus Like any polygon, the perimeter is the total distance around the outside, which can be found by adding together the length of each side. In the case of a rhombus, all four sides are the same length by definition, so the perimeter is four times the length of a side. Or as a formula: perimeter = 4S where: S is the length of any one side
Area of Rhombus (given the length of the diagonals) A rhombus is a 4-sided polygon that has 4 equal sides. The diagonals of a rhombus bisects each other at right angles. Area of rhombus = product of diagonals A= ½ x 1st diagonal x 2nd diagonal
Instead of using the common Rhombus formula, we can also use : - Trapezoid formula - Triangle formula - Parallelogram formula - Rectangle formula
Rhombus Problems (normal) Area of the yellow rhombus : 54 cm 2 Diagonal 1 (yellow rhombus) : 9 cm Find the area of the orange area without the yellow area !!! 12 cm 16 cm
R HOMBUS P ROBLEMS (N ORMAL ) a) Find the area of big rhombus!! b) Find the area of the green rhombus !!! 39 cm 24 cm
a) Find the area of the orange rhombus !!! b) Find the area of the blue area !!! 24 cm 32 cm
The size of the obtuse angle of a rhombus is twice the size of its acute angle. The side length of the rhombus is equal to 10 km. a) Find its angle b) Some stores are going be built along the rhombus perimeter and its diagonall. Distance every store is 10 m. How much store it will be at the rhombus ???
R HOMBUS P ROBLEMS ( UNIQUE ) All 1 st diagonal of the rhombus is 48 m. The area of the rhombus is 864 cm 2. a) The area of the yellow rectangle b) Pretend, that the yellow rectangle area is gonna be planted with trees that the distance of every tree is 1 m and the perimeter of the parallelogram is gonna planted by trees too with the distance of every tree is 2 m. How many trees will be there in the parallelogram ????